Fig.
S9. Macroeconomic commodity-flow networks.
(A) U.S. interstate commodity flow.(10)
The central 15 states (white), along with the surrounding edge-zone of 19 immediately
contiguous states (light gray), were analyzed. Core and edge areas for
USA15 states are listed in Table S5 connection matrix below.
(B) European international commodity flow.(11)
The central 8 countries (white), along with a fragmentary surrounding edge-zone
of 6 immediately contiguous countries (light gray), were analyzed as pilot data.

Table S5. Combined "connection" and adjacency matrix for
U.S. interstate commodity flow (1997 Survey Sample). The series of 15
core states shown above in Fig. S9A is listed (KS - OK), in
the order in which the areas are successively added to the analysis.
They are followed by the set of 19 edge states for the total core (TX - LA).
Cell values are in $ millions. An all-or-nothing cutoff threshold was
set to yield approximately the same connectivity density as macaque and cat
cortex above (see Table S7): If "export"
+ "import" flow between two states exceeds $ 1,500,000,000, a connection is
recorded; sub-threshold economic transactions between the state of a row and
the state of a columncount as no connection.
Cell values in bold designate topological contiguity of the two states, as in
Fig. S9A.

Fig. S10. Size Law performance for commodity flow among
15 U.S. states (BTS). The system of components here is a core of contiguous
economic zones as in Fig. S9, with "connections" and adjacencies
as in Table S5. For evaluation of how well total interconnection
costs are minimized, optimality-measure is conformance of the system to the
"all or nothing" adjacency rule: each layout is scored in terms of its
number of violations of the rule. A series of nested compact subsets of
the set of zones was generated (order of successive states added is as in Table
S5). Each subset of the actual layout was compared with all possible
alternative layouts of that subset for adjacency-rule optimality (14 and 15-element
sets were each compared only with random samples of 109 alternative
layouts).

The US system attains better
connection-optimization than macaque or cat visual cortex, with no layouts
better than actual found in a 1 billion sample. This may appear to vindicate the
"invisible hand" of laissez-faire economics. However, the "Actual
layout" curve departs markedly from the Size Law pattern; smaller subsets
already attain perfect optimality--i.e., an
optimality ratio of 0, with no alternative layouts better than the actual
one. This breakdown suggests the macroeconomic networks are
optimized locally, unlike the cortex (and some chip) networks. For
calibration, the "Scrambled layout" (broken-line) curve, for the 15 U.S.
states with their adjacencies randomly shuffled, shows the usual "flat"
unoptimized pattern.